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Unconditionally stable explicit schemes for the approximation of conservation laws. (English) Zbl 0999.65093
Fiedler, Bernold (ed.), Ergodic theory, analysis, and efficient simulation of dynamical systems. Berlin: Springer. 775-803 (2001).
Summary: We consider explicit schemes for homogeneous conservation laws which satisfy the geometric Coqurant-Friedrichs-Lewy (CFL) condition in order to guarantee stability but allow a time step with CFL-number larger than one. A brief overview over existing unconditionally stable schemes for hyperbolic conservation laws is provided, although the focus is on R. J. LeVeque’s large time step Godunov scheme [Numerical methods for conservation laws (1990; Zbl 0723.65067)]. For this scheme we explore the question of entropy consistency for the approximation of one-dimensional scalar conservation laws with convex flux function and describe a possible way to extend the scheme to the two-dimensional case. Numerical calculations and analytical results show that an increase of accuracy can be obtained because the error introduced by the modified evolution step of the large time step Godunov scheme may be less important than the error due to the projection step.
For the entire collection see [Zbl 0968.00013].

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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